Geometry 6.1 Angles of Polygons

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Presentation transcript:

Geometry 6.1 Angles of Polygons

Diagonals A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Ex. 1. How many diagonals can we draw in the rectangle?

Triangles Ex. 2. How many diagonals can be drawn in the triangle?

A m<A = m<B = B C 3xº 72º xº What is the sum of the interior angles of a triangle? Ex. 3. Find the missing angles. A m<A = m<B = 3xº 72º xº B C

Quadrilaterals… Draw all possible diagonals from Vertex A. How many triangles were formed as a result? What do you think this means for the sum of the interior angles of a quadrilateral? A

Polygons Hexagon Octagon Nonagon Decagon

SI = (n – 2) • 180º INTERIOR ANGLE SUM Ex. 4. Find the sum of the interior angles of a convex octagon. Ex. 5. Find the sum of the interior angles of a convex 15-gon.

Ex. 6. Solve for x. Ex. 7. Solve for y. 120º xº 48º 2xº 139º 5yº 71º 9yº 92º

Regular Polygons º A REGULAR polygon is Equilateral and Equiangular (all sides and all angles ). To Find the measure of each Interior Angle of a regular convex polygon. º

Ex. 8. Find the measure of each angle in a regular convex octagon. Ex Ex. 8. Find the measure of each angle in a regular convex octagon. Ex. 9. The measure of each interior angle of a regular polygon is 165º. How many sides does the polygon have?

Exterior Angles m<1 + m<2 = 180º The Exterior Angle of any polygon forms a linear pair with an Interior angle of a polygon. Ex. <1 is an exterior angle. <1 and <2 form a linear pair. <1 <2 m<1 + m<2 = 180º

The sum of the exterior angles of a convex polygon =360º ALL Exterior Angles of EVERY polygon add up to 360º

Ex. 10. What is the sum of the exterior angles of a convex triangle? Ex. 11. What is the sum of the exterior angles of a convex 300-gon?

Regular Polygons To Find the measure of each Exterior Angle of a regular convex polygon.

Ex. 12. Find the measure of each exterior angle of a regular heptagon Ex. 12. Find the measure of each exterior angle of a regular heptagon. Ex. 13. The measure of each exterior angle of a regular polygon is 40º. How many sides does it have?

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